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Question-115736

Question Number 115736 by gab last updated on 28/Sep/20 Answered by Dwaipayan Shikari last updated on 28/Sep/20 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} }{\mathrm{2n}^{\mathrm{2}} \left(\mathrm{2i}\right)}.\left(\mathrm{e}^{\mathrm{i}\pi\mathrm{n}} −\mathrm{e}^{−\mathrm{i}\pi\mathrm{n}} \right)\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{sin}\left(\pi\mathrm{n}\right)=\frac{\mathrm{e}^{\mathrm{i}\pi\mathrm{n}} −\mathrm{e}^{−\mathrm{i}\pi\mathrm{n}}…

Calcul-n-3-2n-1-n-n-2-n-2-

Question Number 181260 by lapache last updated on 23/Nov/22 $${Calcul}\: \\ $$$$\underset{{n}=\mathrm{3}} {\overset{+\infty} {\sum}}\:\frac{\mathrm{2}{n}−\mathrm{1}}{{n}\left({n}+\mathrm{2}\right)\left({n}−\mathrm{2}\right)}=…?? \\ $$ Answered by SEKRET last updated on 23/Nov/22 $$\frac{\mathrm{89}}{\mathrm{96}} \\…